Question

How do you simplify `(5sqrt[2] + 3)(sqrt[2] – 2sqrt[3])`?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(5sqrt(2)) + color(red)(3))(color(blue)(sqrt(2)) - color(blue)(2sqrt(3)))` becomes:

`(color(red)(5sqrt(2)) xx color(blue)(sqrt(2))) - (color(red)(5sqrt(2)) xx color(blue)(2sqrt(3)))) + (color(red)(3) xx color(blue)(sqrt(2))) - (color(red)(3) xx color(blue)(2sqrt(3))))`

`(5 * 4) - (10sqrt(2)sqrt(3)) + 3sqrt(2) - 6sqrt(3)`

`20 - (10sqrt(2)sqrt(3)) + 3sqrt(2) - 6sqrt(3)`

We can use this rule of radicals to complete the simplification:

`sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))`

`20 - (10sqrt(color(red)(2))sqrt(color(blue)(3))) + 3sqrt(2) - 6sqrt(3)`

`20 - (10sqrt(color(red)(2)*color(blue)(3))) + 3sqrt(2) - 6sqrt(3)`

`20 - 10sqrt(6) + 3sqrt(2) - 6sqrt(3)`